YΔ- And ΔY-transformation
In graph theory, ΔY- and YΔ-transformations (also written delta-wye and wye-delta) are a pair of operations on Graph (discrete mathematics), graphs. A ΔY-transformation replaces a triangle graph, triangle by a vertex of vertex degree, degree three; and conversely, a YΔ-transformation replaces a vertex of degree three by a triangle. The names for the operations derive from the shapes of the involved subgraphs, which look respectively like the letter Y and the Greek capital letter Delta (letter), Δ. A YΔ-transformation may create multi-edge, parallel edges, even if applied to a simple graph. For this reason ΔY- and YΔ-transformations are most naturally considered as operations on multigraphs. On multigraphs both operations preserve the edge count and are exact inverses of each other. In the context of simple graphs it is common to combine a YΔ-transformation with a subsequent ''normalization step'' that reduces parallel edges to a single edge. This may no longer preserve t ...
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